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Simplifying 4x2 + 4x + -51 = 0 Reorder the terms: -51 + 4x + 4x2 = 0 Solving -51 + 4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.75 + x + x2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + x + 12.75 + x2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + x + x2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x + x2 = 0 + 12.75 x + x2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 x + x2 = 12.75 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 12.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 12.75 + 0.25 Combine like terms: 12.75 + 0.25 = 13 1.25 + x2 = 13 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 0.5) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 0.5 = 3.605551275 Simplifying x + 0.5 = 3.605551275 Reorder the terms: 0.5 + x = 3.605551275 Solving 0.5 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.605551275 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.605551275 + -0.5 x = 3.605551275 + -0.5 Combine like terms: 3.605551275 + -0.5 = 3.105551275 x = 3.105551275 Simplifying x = 3.105551275Subproblem 2
x + 0.5 = -3.605551275 Simplifying x + 0.5 = -3.605551275 Reorder the terms: 0.5 + x = -3.605551275 Solving 0.5 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.605551275 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.605551275 + -0.5 x = -3.605551275 + -0.5 Combine like terms: -3.605551275 + -0.5 = -4.105551275 x = -4.105551275 Simplifying x = -4.105551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.105551275, -4.105551275}
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